Final answer:
Raquel has 14 dimes. She has a total of $3.80, with $2.40 in nickels (48 nickels at $0.05 each). The remaining $1.40 must be in dimes, and since each dime is $0.10, dividing $1.40 by $0.10 gives us 14 dimes.
Step-by-step explanation:
The student's question involves determining the number of dimes Raquel has, given that she has collected $3.80 in nickels and dimes and has exactly 48 nickels.
First, we need to calculate the total value of the 48 nickels. Since one nickel is worth 5 cents, the total value can be calculated as follows:
- Value of one nickel = $0.05
- Value of 48 nickels = 48 × $0.05 = $2.40
Now we know that the total amount collected is $3.80, out of which $2.40 is in nickels. To find out how much is in dimes, we subtract the value of the nickels from the total amount:
Total amount - Value of nickels = Amount in dimes
$3.80 - $2.40 = $1.40
Since one dime is worth 10 cents, we calculate the number of dimes by dividing the remaining amount by the value of one dime:
Number of dimes = Amount in dimes ÷ Value of one dime
Number of dimes = $1.40 ÷ $0.10 = 14 dimes
Therefore, Raquel has 14 dimes.